Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

APS

Impact of the ^87Rb singlet scattering length on suppressing inelastic collisions

J. P. Burke, John L. Bohn, Brett D. Esry, Chris H. Greene

Published Apr 1, 1997• 1 citation
OpenAlex

Abstract

A computation of $^{87}\mathrm{\ensuremath{-}}^{87}$Rb spin-exchange rate constants as functions of the two-body singlet scattering length ${\mathrm{a}}_{\mathrm{s}}$ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for ${\mathrm{a}}_{\mathrm{s}}$. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the $^{87}\mathrm{Rb}$ singlet scattering length (74--102 a.u.).

Related papers

Impact of the Rb87 singlet scattering length on suppressing inelastic collisions

James P. Burke, John L. Bohn, Brett D. Esry +1 more

A computation of $^{87}\mathrm{\ensuremath{-}}^{87}$Rb spin-exchange rate constants as functions of the two-body singlet scattering length ${\mathrm{a}}_{\mathrm{s}}$ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for ${\mathrm{a}}_{\mathrm{s}}$. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the $^{87}\mathrm{Rb}$ singlet scattering length (74--102 a.u.).

Physical Review A•Apr 1, 1997•81 citations

Role of collisions in creation of overlapping Bose condensates

S. J. J. M. F. Kokkelmans, H. M. J. M. Boesten, BOUDEWIJN J. VERHAAR

We study the elastic scattering length and inelastic decay rate associated with collisions of $^{23}\mathrm{Na}$ and $^{87}\mathrm{Rb}$ atoms in different hyperfine states: one with atoms in the |f=2,${\mathrm{m}}_{\mathrm{f}}$=2〉 and one with atoms in the |f=1,${\mathrm{m}}_{\mathrm{f}}$=-1〉 state. For Na the real part of the ${\mathrm{a}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ scattering length for |22〉+|1-1〉 collisions is predicted to be positive and equal to 65\ifmmode\pm\else\textpm\fi{}5 Bohr length units ${\mathrm{a}}_{0}$ for small B. The zero-temperature low-field decay rate is of the order of a typical exchange rate: ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$=(1.5\ifmmode\pm\else\textpm\fi{}0.7)${10}^{\mathrm{\ensuremath{-}}11}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, showing that a two-condensate experiment is not feasible for a Na gas sample in a static magnetic trap. For the case of Rb atoms the present knowledge of the singlet interaction does not allow a similar calculation. The extreme suppression of ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ demonstrated by a recent experiment is shown to be very restrictive for the value of the singlet accumulated phase.

Physical Review A•Mar 1, 1997•39 citations

Low-energy scattering properties of ground-state and excited-state positronium collisions

Michael D. Higgins, K. M. Daily, Chris H. Greene

Low-energy elastic and inelastic scattering in the Ps($1s$)-Ps($2s$) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum $L=0$ and parity equal to $+1$. The $s$-wave scattering lengths for the asymptotic Ps($1s$)-Ps($2s$) channel are calculated for each spin configuration. Results obtained for the $s$-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and ${a}_{\mathrm{ST}}=9.7(2){a}_{0}$ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.

arXiv:1904.04295•Journal of Physics Conference Series•Jul 29, 2019•4 citations

Collisional Stability of Double Bose Condensates

Paul S. Julienne, Frederick H. Mies, Eite Tiesinga +1 more

This paper presents quantitative calculations of collisional loss rates for pure $^{23}N\mathrm{a}$ or $^{87}R\mathrm{b}$ atoms in a binary mixture of hyperfine states $|F,M〉$. We find that the recent observation of a dual Bose condensate consisting of $^{87}R\mathrm{b}$ $|1,\ensuremath{-}1〉$ and $|2,2〉$ atoms is unique and will not occur in Na. We attribute this to the unexpectedly small inelastic spin-exchange rate associated with $^{87}R\mathrm{b}$ s-wave hyperfine collisions. This fortuitous result arises from nearly equal $(5.45\ifmmode\pm\else\textpm\fi{}0.26\mathrm{nm})$ scattering lengths for two colliding $^{87}R\mathrm{b}$ atoms in their $|1,\ensuremath{-}1〉$ or $|2,2〉$ states.

Physical Review Letters•Mar 10, 1997•123 citations

Scattering lengths for Li–Cs, Na–Cs, K–Cs, and Rb–Cs ultracold collisions

A.L.M. Zanelatto, Evandro Marcos Saidel Ribeiro, Reginaldo de Jesus Napolitano

We present triplet and singlet scattering lengths for X--133Cs collisions (X=6,7Li, 23Na, 39,40,41K, and 85,87Rb). We consider the short-range potential-energy curves based on high-quality ab initio calculations and the long-range potential described by accurate dispersion coefficients available in the literature. Using a Fermi function to smoothly connect the short- and long-range terms we construct the potential for all R and evaluate the scattering length for each mixed species X--Cs. In particular, we predict that the cross section for inelastic processes between 23Na and 133Cs and between 40K and 133Cs will be small as compared with the respective elastic cross sections.

The Journal of Chemical Physics•Jul 1, 2005•14 citations

Triplet s-wave resonance in Li6 collisions and scattering lengths of Li6 and Li7

E. R. I. Abraham, W. I. McAlexander, Jordan M. Gerton +3 more

The triplet s-wave scattering length of $^{6}\mathrm{Li}$ is determined using two-photon photoassociative spectroscopy of the diatomic a${\mathrm{}}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ state of $^{6}\mathrm{Li}_{2}$. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)${\mathrm{a}}_{0}$, where ${\mathrm{a}}_{0}$ is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ determined from this and our previous spectroscopic investigations is given.

Physical Review A•May 1, 1997•190 citations
A computation of 87\ensuremath−87^{87}\mathrm{\ensuremath{-}}^{87}87\ensuremath−87Rb spin-exchange rate constants as functions of the two-body singlet scattering length as{\mathrm{a}}_{\mathrm{s}}as​ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for as{\mathrm{a}}_{\mathrm{s}}as​. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the 87Rb^{87}\mathrm{Rb}87Rb singlet scattering length (74--102 a.u.).
A computation of $^{87}\mathrm{\ensuremath{-}}^{87}$Rb spin-exchange rate constants as functions of the two-body singlet scattering length as{\mathrm{a}}_{\mathrm{s}}as​ demonstrates that the inelastic collision rate is suppressed over a small range of the possible values for as{\mathrm{a}}_{\mathrm{s}}as​. A two-channel model relates this inelastic suppression to an interference phenomenon, manifested in the near coincidence of the singlet and triplet scattering lengths. This mechanism explains the diminished rates measured in recent ``double-trap'' experiments. Combining information extracted from these rates and from previous scattering length measurements allows us to place bounds on the 87Rb^{87}\mathrm{Rb}87Rb singlet scattering length (74--102 a.u.).
We study the elastic scattering length and inelastic decay rate associated with collisions of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb atoms in different hyperfine states: one with atoms in the |f=2,mf{\mathrm{m}}_{\mathrm{f}}mf​=2〉 and one with atoms in the |f=1,mf{\mathrm{m}}_{\mathrm{f}}mf​=-1〉 state. For Na the real part of the ${\mathrm{a}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ scattering length for |22〉+|1-1〉 collisions is predicted to be positive and equal to 65\ifmmode\pm\else\textpm\fi{}5 Bohr length units a0{\mathrm{a}}_{0}a0​ for small B. The zero-temperature low-field decay rate is of the order of a typical exchange rate: ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$=(1.5\ifmmode\pm\else\textpm\fi{}0.7)${10}^{\mathrm{\ensuremath{-}}11}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, showing that a two-condensate experiment is not feasible for a Na gas sample in a static magnetic trap. For the case of Rb atoms the present knowledge of the singlet interaction does not allow a similar calculation. The extreme suppression of ${\mathrm{G}}_{(22)+(1\mathrm{\ensuremath{-}}1)}$ demonstrated by a recent experiment is shown to be very restrictive for the value of the singlet accumulated phase.
Low-energy elastic and inelastic scattering in the Ps(1s1s1s)-Ps(2s2s2s) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum L=0L=0L=0 and parity equal to +1+1+1. The sss-wave scattering lengths for the asymptotic Ps(1s1s1s)-Ps(2s2s2s) channel are calculated for each spin configuration. Results obtained for the sss-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and aST=9.7(2)a0{a}_{\mathrm{ST}}=9.7(2){a}_{0}aST​=9.7(2)a0​ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.
This paper presents quantitative calculations of collisional loss rates for pure 23Na^{23}N\mathrm{a}23Na or 87Rb^{87}R\mathrm{b}87Rb atoms in a binary mixture of hyperfine states ∣F,M〉|F,M〉∣F,M〉. We find that the recent observation of a dual Bose condensate consisting of 87Rb^{87}R\mathrm{b}87Rb $|1,\ensuremath{-}1〉$ and ∣2,2〉|2,2〉∣2,2〉 atoms is unique and will not occur in Na. We attribute this to the unexpectedly small inelastic spin-exchange rate associated with 87Rb^{87}R\mathrm{b}87Rb s-wave hyperfine collisions. This fortuitous result arises from nearly equal $(5.45\ifmmode\pm\else\textpm\fi{}0.26\mathrm{nm})$ scattering lengths for two colliding 87Rb^{87}R\mathrm{b}87Rb atoms in their $|1,\ensuremath{-}1〉$ or ∣2,2〉|2,2〉∣2,2〉 states.
We present triplet and singlet scattering lengths for X--133Cs collisions (X=6,7Li, 23Na, 39,40,41K, and 85,87Rb). We consider the short-range potential-energy curves based on high-quality ab initio calculations and the long-range potential described by accurate dispersion coefficients available in the literature. Using a Fermi function to smoothly connect the short- and long-range terms we construct the potential for all R and evaluate the scattering length for each mixed species X--Cs. In particular, we predict that the cross section for inelastic processes between 23Na and 133Cs and between 40K and 133Cs will be small as compared with the respective elastic cross sections.
The triplet s-wave scattering length of 6Li^{6}\mathrm{Li}6Li is determined using two-photon photoassociative spectroscopy of the diatomic a3{\mathrm{}}^{3}3${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ state of 6Li2^{6}\mathrm{Li}_{2}6Li2​. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160\ifmmode\pm\else\textpm\fi{}250)a0{\mathrm{a}}_{0}a0​, where a0{\mathrm{a}}_{0}a0​ is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving 6Li^{6}\mathrm{Li}6Li and 7Li^{7}\mathrm{Li}7Li determined from this and our previous spectroscopic investigations is given.